No evidence from seismic tomography for wave speed. changes during the Mount Etna eruption

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1 submitted to Geophys. J. Int. No evidence from seismic tomography for wave speed changes during the Mount Etna eruption Ceri Nunn,, Bruce R. Julian, Gillian R. Foulger, Najwa Mhana Dept. of Earth Sciences, Durham University, South Road, Durham, DH LE, U.K. Dept. of Earth and Environmental Sciences, Geophysics Section, Ludwig-Maximilians-Universität, Munich, Germany SUMMARY Repeat seismic tomography has been used to infer temporal changes in the seismic wave speeds of rocks in volcanic and geothermal regions. Researchers commonly use earthquakes as sources. Data are separated into suitable time periods. Data from these periods, or epochs, are inverted independently, and then compared. However, repeated inversions for a region are expected to differ even if the structure did not change, due to variations in the seismic ray distribution and observational errors. We use a new tomography program, tomod, which inverts multiple data sets simultaneously, and seeks to minimize the difference between the models for different epochs as well as the misfit between the observed and predicted arrival times. tomod can therefore determine what changes are truly required by the data. As an example, we investigated an eruption cycle prior to, and during, the October -January flank eruption at Mount Etna in Sicily. Independently inverted data sets indicated changes in the compressional wave speed (V P ) of up to % during the eruption cycle. However, tomod fit the data from different epochs to the same structural model, at the same time reducing the arrival time rms residuals

2 Nunn et al. by %. In contrast, the rms residuals reduced by only 8 % for the independently inverted epochs. Therefore we infer no temporal changes to the seismic wave speeds are required by the data during this eruption cycle. We also show that the absolute wave speeds derived depend on the inversion parameterisation. This result indicates that even large differences between models generated from independently inverting epochs may be suspect. Key words: Tomography; Volcano monitoring; Seismic tomography; Volcano seismology; INTRODUCTION Repeat tomography, also known as -D or time-lapse tomography, has been used to infer changes in the elastic properties of rocks in volcanic and geothermal regions, and in oil reservoirs. Laboratory experiments indicate that changes in physical properties such as temperature, stress, pore pressure and cracks, affect the elastic properties of rocks (e.g. Mavko 98; Sato et al. 989; Sanders et al. 99). Julian et al. (998) and Foulger et al. () used repeat seismic tomography to monitor gas concentrations in geothermal and volcanic systems. Patanè et al. () monitored the seismic velocities before and during the flank eruption of Mount Etna from October to January. They reported that the ratio of the compressional and shear seismic wave speeds ( ) changed by about % throughout a volume about 7 long over a depth range of about. Repeated inversions for a region would differ even if the structure did not change, due to variations in the seismic ray distribution and observational errors. We investigate possible changes in structure using a new seismic-tomography program, tomod (Julian & Foulger ), which we apply to observational data for the first time. tomod uses a novel approach, which makes it possible to determine what changes are truly required by the data. The program inverts multiple data sets simultaneously, seeking to minimize the difference between the models for different epochs as well as the misfit between the observed and predicted arrival times.

3 Geophys. J. Int.: Time-dependent seismic tomography of Mt. Etna Repeat seismic tomography is an inverse problem, where seismic wave speeds are inferred from observations, and practitioners commonly seek the best solution implied by the data. Tarantola () argued that observations should only be used to falsify possible solutions, not to deduce any particular solution. Consequently, if two epochs of data can fit the same model equally well, it is not justified to infer changes between epochs. Mount Etna is a basaltic stratovolcano near the east coast of Sicily that rises to about m above sea level (Fig. ). It lies in a complex geodynamic setting that results from interactions between the African and Eurasian plates (Faure ). Etna degasses nearly continuously from its summit craters, (Allard et al. 99), and produces frequent basaltic lava flows and a variety of eruption styles including Strombolian activity (Pering et al. ). Tomographic models show a central high-velocity region (Patanè et al. ). Aloisi et al. () also imaged low compressional wave velocities (V P ) values to the west and east, which they interpreted as highly fractured, weak rocks. On the basis of magnetotelluric surveying, Mauriello et al. () inferred there is no permanent magma chamber within the top, and suggested that a slowly-cooling dyke reaches depths of at least in the central sector. Chiarabba et al. () suggest that magma ascends through the crust via a small, high-velocity conduit. They detect no large, low-velocity anomaly interpretable as a magma chamber in the upper 8. Sicali et al. () found well-defined earthquake clusters preceding the July August eruption, which they interpreted as evidence of magma migration from 8 below sea level towards a shallower zone. We investigated a flank eruption that lasted from 7 October to 8 January. The episode included intense eruptive activity, fire fountains, and fairly continuous tephra fallout (Patanè et al. ). As described above, Patanè et al. () compared models derived from data collected before and during the eruption, and inferred structural changes brought about by the eruption. We applied tomod to test whether the data require these changes.

4 Nunn et al... a).... b) 7.8 Elevation, m Figure. a) Map of the island of Sicily and vicinity. Black box: study area at Mount Etna. b) Expanded-scale map of the study area. Black triangles: seismometers; black lines: elevation contours (interval m); yellow stars: approximate locations from Neri et al. () of eruptive fissures along the NE and south rifts that opened during the eruption (Walter et al. ). FOUR-DIMENSIONAL TOMOGRAPHY Repeat tomography, also known as -D or time-lapse tomography, has been used for many years to monitor changes in oil reservoirs (McGillivray ; Byerley et al. 9). Experiments have used controlled sources or virtual sources. In geothermal and volcanic areas, earthquakes are often plentiful and can be used as sources. For example, Foulger et al. (997) found decreases of up to % in the ratio between 99 and 99 at The Geysers geothermal reservoir in northern California. Gunasekera et al. () found that the change was caused primarily by a decrease in V P, an expected consequence of an increase in porefluid compressibility caused by decreasing pressure in the reservoir. Foulger et al. () reported a negative anomaly below sea level beneath Mammoth Mountain, Long Valley caldera, California, interpreted as a CO reservoir. They attempted to deal with the inherent sampling problem of seismic tomography for different epochs by starting from a combined data set which they parameterized with relatively low damping, to allow reasonably strong variation within the model. They used this model as a starting model, and independently inverted two epochs using stronger damping, in order to discourage all but

5 Geophys. J. Int.: Time-dependent seismic tomography of Mt. Etna the most significant model changes. However, this procedure is still fundamentally unable to distinguish between true temporal variations and the effects of random observational errors, or to provide estimates of uncertainty. Previous work on Etna found well-defined regions with anomalously low ratios between the compressional and shear wave speeds ( ratio as low as.) beneath the centralsouthern and northeastern slopes of Etna during the October January flank eruption, which were absent during the pre-eruptive period (Patanè et al. ). During the same eruptive phase, high ratios were observed beneath the eastern and southeastern flanks of the volcano. Patanè et al. () attributed the low ratios to intrusive volatile-rich basaltic magmas and the high ratios during the same eruptive period to the rapid migration of fluids from the intrusion zone into the fractured regions beneath the flanks. The low ratios corresponded to a region where independent geodetic data modelling suggested dyke intrusions during (Aloisi et al. ; Patanè ). DATA AND METHODS We used arrival-time data of Patanè et al. (), although we applied different selection criteria and relocated the earthquakes. We used data from 8 seismic stations from the permanent and temporary networks (Fig. ) operated by the Istituto Nazionale di Geofisica e Vulcanologia Sezione di Catania (INGV-CT), including three-component digital stations, single-component analogue and three-component analogue stations. During the study period, INGV-CT moved some of the stations as the seismicity migrated. We used a layered model (Model A, Chiarabba et al. ) as a starting model for our inversions and for locating the earthquakes (Fig. ). Our selection criteria for earthquakes required at least four paired P- and S-wave observations, and an azimuthal gap between adjacent stations < degrees. We plotted Wadati diagrams for each event, and removed obvious outliers. The average ratio obtained from the Wadati diagrams was.7, but there was a strong scatter and ratios between about.7 and.8 are consistent with

6 Nunn et al. Model A, Chiarabba Interpolated (grid nodes) Interpolated (every ) Depth, V p, /s Figure. One-dimensional V P models for the Etna region. Blue line: layered model A of Chiarabba et al. (); Red dots: interpolated values at the depths of grid nodes in our initial -D model; Green dots: interpolated values at - intervals, used for locating earthquakes. the data. The data scatter for individual events is generally too high to estimate the ratio. Fig. b shows earthquake epicentres after relocation using a ratio of.7 and discarding events with a root-mean-square residual (rms) greater than. s. Earthquake hypocentres are clustered, with the majority located about east of the central craters, in a volume that plunges eastward and reaches depths of around 8. Following Patanè et al. (), we split the eruptive cycle into three epochs, based on ground deformation and SO flux (Fig. a). During Pre-eruptive Period I ( August to April ), which followed an earlier flank eruption, the ground subsided and the SO flux was low. During Pre-eruptive Period II ( May to October ) the ground uplifted and the SO flux remained low. The period was a recharging phase (Patanè ). The Eruptive Period (7 October to 8 January ) included a flank eruption, a dramatic increase in the SO flux, and an increase in seismicity. We also selected a group of earthquakes from, distributed within the volume as uniformly as possible (Fig. :c). The final numbers of good-quality earthquakes for and for the three

7 Geophys. J. Int.: Time-dependent seismic tomography of Mt. Etna 7 a) b) Relocated Earthquakes Focal Depth,.8.. c) (Balanced) d) Pre eruptive Period I e) Pre eruptive Period II f) Eruptive Period Figure. a) Chronology of events at Mount Etna during the period August January covered by this study, modified from (Patanè et al. ). Blue line: Changes in elevation along a central-western baseline measured using GPS (Patanè ); Red line: SO flux, in tonnes per day (t/d). b) Our locations for earthquakes from November to December. The map, and those below, cover the same area as Fig. b. c) Earthquakes used in tomographic inversion, selected to improve uniformity of coverage. d), e), and f): Subsets of earthquakes in each epoch. periods of the eruptive cycle were,, and (Fig. : c, d, e, & f). The earthquakes from the eruptive cycle are strongly clustered. Although the numbers of earthquakes in the epochs are relatively small, the abundance of stations ensured that the ray density is greater than seismic rays per node (within the volume surrounding each grid node) across much of the central area (Fig.S, Supplementary Material).. Inverting Epochs Independently We began by independently inverting data from and from the three periods (Fig. : c, d, e, & f), using the tomography program SIMULA (Evans et al. 99), which uses the an approximate ray-tracing method and an iterative damped least-squares method. It estimates the locations of the earthquakes, the ray paths, and the -D V P and structures, which are parameterized on a -D Cartesian grid, using trilinear functions to interpolate values between grid nodes. The nodes were spaced every horizontally

8 8 Nunn et al. and covered a 8 x area. Vertical nodal spacing was from - to 8 depth, with additional nodes at, and depths. The grid included all the earthquakes and stations. We used a one-dimensional initial V P model (Fig. ) and a ratio of.7... Damping During the iterative inversion process, we applied damping constraints to limit the magnitudes of changes made to the seismic-event origins and the wave-speed models. We used an empirical approach to set the damping. For each data set, we ran several inversions using different damping values for one iteration, and compared the reduction in the rms residual to the variance of the output model (Fig. ). Preferred values should improve the data fit without causing unnecessary increases in the model variance. In some cases, the S- phase arrival-time residuals increased while the combined residuals for both P and S-phases residuals decreased. If necessary, we used higher damping values to prevent this problem.. Inverting Epochs Simultaneously The seismic tomography program tomod inverts multiple data sets simultaneously, seeking to minimise the difference between the models for different epochs as well as the misfit between the observed and predicted arrival times, using the algorithm given by Julian & Foulger (). We used the same grid size, initial wave-speed model and groups of earthquakes (Fig. ) as described above. We inverted Pre-eruptive Period I simultaneously with the Eruptive Period, and Pre-eruptive Period II simultaneously with the Eruptive Period. Since the method requires two sets of earthquakes, we inverted the data using the same group of earthquakes twice.

9 Geophys. J. Int.: Time-dependent seismic tomography of Mt. Etna 9. - P and S arrival time rms, s Vp Model Variance, - (/s). Figure. Root-mean-square (rms) arrival-time residual vs. model variance after one iteration of SIMULA, using earthquakes from, for different V P damping-parameter values. Model variance is a measure of the strength of the spatial variations in the V P model. It is calculated from the differences of the V P perturbations from the average at each depth. Each perturbation is squared and then averaged for the layer. Finally the layer averages are summed and divided by the number of layers. The red circle shows the value for the final run. The Supplementary Material includes simular curves for the tomod inversions and the remaining SIMULA inversions. At each iteration step tomod attempts to minimise the following sum: n df χ + ɛ V epochs nodes [ ( VP ) ( ) ] VS + σ VP σ VS [ ( δvp ) ( ) ] δvs + ɛ Epoch + nodes + ɛ Origin σ δvp epochs local events σ δvs [ ( x) + ( y) σ h ( ) ( ) ] z t + + σ z The first term measures the goodness of fit to the data. n df is the corresponding number of degrees of freedom (the number of residuals minus the number of adjustable parameters) and χ is defined as: χ def = data σ t () () () () ( ) tobs t calc () σ

10 Nunn et al. where t obs and t calc are an observed and computed arrival time, σ is the corresponding standard error, the estimated accuracy of the arrival time measurement. We set the standard error to. s for the best-quality arrival times, and to.8 s,. s and. s for lowerquality arrivals. The remaining terms are damping constraints, with the upper-case symbol referring to changes from iteration to iteration and the lower-case symbol δ referring to temporal changes (from epoch to epoch). The second term constrains changes from iteration to iteration in the seismic wave speeds in the model. The parameter ɛ V adjusts the strength of the constraint. The quantities σ VP and σ VS are a priori standard errors that control the sensitivities to compressional and shear wave speeds. We set both of these quantities to. /s. The third term constrains changes in the seismic wave speeds between epochs. The parameter ɛ Epoch adjusts the strength of the constraint. The standard errors σ δvp and σ δvs are a priori standard errors that control the sensitivity to wave speed changes with time. We set both of these quantities to. /s. The fourth term constrains changes in hypocentre locations and origin times. The parameter ɛ Origin adjusts the strength of the constraint. x, y, z, and t are the changes to the hypocentral coordinates and the origin time of a seismic event. The parameters σ h, σ z and σ t control the sensitivity to the horizontal positions, vertical positions, and origin times of the events. We set these parameters to.,., and. s respectively. We set the ɛ V parameter, which adjusts the strength of the constraint on the perturbations to the seismic wave speeds for each iteration, using the same empirical approach as for the SIMULA inversions. Fig.S in the Supplementary Material contains trade-off curves for both programs. As with SIMULA, for some inversions, the S-phase arrival-time rms residual increased while the overall rms residual fell. If necessary, we used higher damping values to prevent this problem. We kept the ɛ Epoch parameter, which controls the strength of the differences between epochs, at its default value of. Changing this parameter made almost no difference to the improvement in the data residuals.

11 Geophys. J. Int.: Time-dependent seismic tomography of Mt. Etna RESULTS Fig. compares results from SIMULA and tomod for earthquakes from. The V P results are broadly similar, although with tomod recovering lower structural variation (Fig. : column and column ). The results show a zone of high wave speeds southeast of the central craters at sea level, and plunging steeply to the east. This zone is in approximately the same location as most of the earthquakes (Fig. : top right). A ring of slower V P values surrounds the central zone (this is particularly clear in Fig. : top left). The ratios show much greater variation between the results from the two programs, and we found that SIMULA controlled the variation more strongly than tomod. For SIMULA (Fig. : column ), the variation is small, and the is higher than the initial value of.7 in all areas. For tomod (Fig. : column ) there is more variation. Generally, high ratios are found in areas where V P is high, and low ratios where V P is low. Figs. and 7 compare results from different epochs. We show comparisons between independent inversions, and simultaneous inversions using tomod. Fig. compares Preeruptive Period I with the Eruptive Period. For both periods and both methods, the high-v P central region clearly imaged in Fig. is evident. However, its boundaries are less sharp, and are in slightly different places for the different epochs. The strength of the anomalies is lower than in Fig.. The variation in for each epoch is lower for SIMULA than for tomod. Column of Fig. shows the percentage change in V P between the two epochs, which ranges between -% and +% for SIMULA, but is <.% for tomod. Similarly, despite the larger variation in ratio obtained using tomod, the change between epochs is <.. The results are similar when comparing Pre-eruptive Period II with the Eruptive Period (Fig. 7). We inverted the Eruptive Period twice for tomod: once with Pre-eruptive Period I and once with Pre-eruptive Period II. The model recovered for the Eruptive Period is slightly different for the two cases (Figs and 7).

12 Nunn et al. SIMUL:- TOMOD:- Sea Level Sea Level Depth = Depth = Depth = Depth = Depth = 8 Depth = Figure. Wave-speed models produced using SIMULA (left panels) and tomod (right panels), using earthquakes from (selected to improve uniformity of coverage), at different depths. Columns and show V P results; columns and show. Black lines: m topographic contours. Solid and dashed white contours: ray density greater than or seismic rays per node (within the volume surrounding each grid node) respectively. Masked areas indicate no ray coverage. P-phase ray density is used for columns and and S-phase ray density for columns and. The area is the same as in Fig.. Damping and other parameters strongly affect the strength of the recovered anomalies for both programs.

13 Geophys. J. Int.: Time-dependent seismic tomography of Mt. Etna Pre-eruptive Period I SIMUL Eruptive Period Change Sea Level Pre-eruptive Period I TOMOD Eruptive Period Change Sea Level Figure. Wave-speed models produced using SIMULA (top panels) and tomod (bottom panels), comparing Pre-eruptive Period I and the Eruptive Period, at different depths. For SIMULA, we carried out independent inversions of arrival times from earthquakes from Preeruptive period I (columns and ) and the Eruptive Period (columns and ). For tomod, we inverted the two epochs simultaneously. Columns and show models from the Pre-eruptive Period and columns and the Eruptive Period. Columns and show V P ; columns and show. Column shows the percentage difference between V P values and column the difference between the values for the two epochs. Solid and dashed white contours indicate ray density greater than or seismic rays per model node respectively. Masked areas indicate no ray coverage. P-wave ray density is used for columns, and and S-wave ray density for columns, and. tomod fit the data from the two epochs with almost the same model. Note

14 Nunn et al. Pre-eruptive Period II SIMUL Eruptive Period Change Sea Level Pre-eruptive Period II TOMOD Eruptive Period Change Sea Level Figure 7. As Fig., except comparing Pre-eruptive Period II and the Eruptive Period. The model from the Eruptive Period for SIMULA is repeated from Fig..

15 Geophys. J. Int.: Time-dependent seismic tomography of Mt. Etna Fig. 8 shows the reduction in the arrival-time rms residuals for SIMUL and tomod for both P and S phases for earthquakes from. The overall reduction is similar between the two programs, although the greater reduction for the P-wave arrival times for SIMULA occurs at the expense of the S-wave times, which show almost no reduction. Fig. 9 shows the reduction in the residuals for different epochs. The left column shows epochs inverted independently with SIMULA, and the right column shows epochs inverted simultaneously with tomod. The simultaneously inverted epochs have lower final rms residuals. In the SIMULA results, the S-wave rms residuals increase for both of the pre-eruptive periods, and only reduce slightly for the Eruptive Period. For both programs it was necessary to increase the damping to make a comparable reduction for both the P and S rms residual. The Supplementary Material contains a summary of the parameterisation and the rms residual reduction for all the models (Table S and Table S). DISCUSSION Our results obtained using tomod show that it is possible to fit the data for Pre-eruptive Period I and II and the Eruptive Period for the eruptive cycle using the same V P and structures. The method where data from each epoch are inverted independently recovers differences of the order of a few percent. However, these are not required by the data. No temporal changes to the seismic wave speeds are required by the data during this eruption cycle. Pre-eruptive Period I simultaneously inverted with the Eruptive Period requires no change, and Pre-eruptive Period II simultaneously inverted with the Eruptive Period also requires no change, yet the two Eruptive Period models are slightly different (Figs. and 7). This is expected, and also a good indication that the recovered models are non-unique. With four-dimensional tomography, four scenarios can be considered: ) no change in the subsurface; ) a change that is below a threshold detectable by seismic methods; ) a change that can be successfully detected; ) incorrect assignment of change resulting from experimental error. Changes must have occurred within the subsurface during the

16 Nunn et al. Initial P rms:.9 s 77 Final P rms:. s 77 SIMUL: - Initial S rms:. s Final S rms:. s Initial P rms:.7 s Final P rms:. s TOMOD: - Initial S rms:.9 s Final S rms:.77 s Figure 8. Histograms of the initial and final arrival-time rms residuals for earthquakes from for SIMULA (left) and tomod (right). P-wave residuals are shown in green and S-wave residuals are in blue. The overall reduction in the residuals was 9.% for SIMULA and.% for tomod. The figure shows the number of observations (n) and the initial and final root mean square rms residual for both P and S waves. Differences in the number of ray convergence failures account for the differences in number of observations between the two panels. Small differences in the forward calculation for SIMULA and tomod account for the differences in the initial rms. eruption cycle from August to January. However, these changes were too small to be detected using the experimental setup. As described in the introduction, Patanè et al. () reported changes to of about % throughout a volume about 7 long over a depth range of about between different periods of the eruption cycle. They inferred changes only where the resolution matrix indicated good coverage. However, we attribute these changes to differences in data coverage, and to other observational errors. In addition, the reported changes are probably unrealistic for the eruption. Julian & Foulger () showed that a major problem when comparing tomographic inversion results from two epochs can be differences in seismic ray coverage. Additionally, the strength of the structural anomalies recovered by tomographic inversions depends strongly on factors such as the number of observations and damping used. Differences in coverage

17 Geophys. J. Int.: Time-dependent seismic tomography of Mt. Etna 7 SIMUL - Pre-eruptive Period I Initial P rms: Initial S rms:.7 s.99 s Final P rms:.9 s Final S rms:. s SIMUL - Pre-eruptive period II Initial P rms: Initial S rms:. s. s 97 Final P rms:. s 97 Initial P rms:.7 s 9 Final P rms:. s 9 9 Final S rms:.7 s 9 SIMUL - Eruptive Period Initial S rms:.8 s Final S rms:.8 s TOMOD - Pre-eruptive Period I Initial P rms: Initial S rms:. s.7 s Final P rms:. s Final S rms:.7 s TOMOD - Pre-eruptive Period II Initial P rms: Initial S rms:.8 s.8 s 97 Final P rms:. s 9 Final S rms:.7 s TOMOD - Eruptive Period (vs. Period I) Initial P rms: Initial S rms:.7 s.9 s 8 Final P rms:. s Final S rms:.8 s TOMOD - Eruptive Period (vs. Period II) Initial P rms: Initial S rms:.7 s.9 s 8 Final P rms:. s Final S rms:.8 s Figure 9. Histograms of the initial and final arrival-time rms residuals for SIMUL (left) and tomod (right) for earthquakes from different periods (panels are labeled to indicate data period). The residuals correspond to the models shown in Figs. and 7. The overall residuals reduce by 8 % for the epochs independently inverted with SIMULA and % for the epochs simultaneously inverted with tomod.

18 8 Nunn et al. and dependence on the parameterisation present an additional complication when comparing two epochs. Even if the same general structure is recovered, one epoch is may show greater range from positive to negative anomalies, resulting in a false indication that the structure has changed over time. Small differences between inversions of data from different epochs would be expected even if seismometer distribution and source locations (e.g. by using controlled sources) remained constant. In the future, we will additionally apply the method to controlled sources, to robustly test the differences between models. We interpret our results from inverting data from (Fig. ) to indicate a central igneous core of high-velocity material, surrounded by a ring of less-dense, and less-well consolidated volcanic sediments. Our V P models are generally consistent with earlier tomography, which also show a central high-velocity region (Patanè et al. ; Aloisi et al. ), and magnetotelluric evidence indicating no detectable magma chamber and a slowly-cooling central dyke (Mauriello et al. ). The recovered ratios, from this and other studies, may be unreliable for two reasons. First, the ratios recovered from Wadati diagrams for each event were strongly scattered. Second, for both programs, ratios recovered from inverting the data depended strongly on the damping, and particularly on whether the P and S residuals decreased at a comparable rate. Therefore, the ratios should be used with caution in geological interpretations. CONCLUSIONS tomod provides a robust way to test for structural change between two data epochs. We split earthquakes from the Mt Etna volcanic cycle, which began in and culminated in the October to January flank eruption, into three epochs. By simultaneously inverting data from two epochs, we showed that the data do not require structural change. When we inverted epochs independently, we obtained wave-speed models that differ by % to +%. Therefore, our results suggest that even large changes between epochs recovered from independently inverted data may be suspect. Our work offers a more reliable approach

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